摘要:

SummaryThis note is an attempt to avoid doing the same search for the third time. It happened twice in my life that I wished to prove that the median is located between mean and mode for certainB‐distributions: first in 1953, next in 1976. For arbitrary distributions the result is sometimes referred to as Fechner'stheorem. Of course it does not hold in general. In order to prove the result for particular distributions one can often use an elegant theorem of Timerding. There is a nice relationship with the standardized third central momen

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1978.tb01386.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

摘要:

SummaryTwo random samples of sizenare taken from a set containingNobjects ofHtypes, first with and then without replacement. Letdbe the absolute (L1‐)distance andIthe Kullback‐Leiblerinformation distance between the distributions of the sample compositions without and with replacement. Sample composition is meant with respect to types; it does not matter whether order of sampling is included or not. A bound onIanddis derived, that depends only onn, N, H.The bound onIis not higher than 2I.For fixedHwe haved0,I0 asNif and only ifn/N0. LetWrbe the epoch at which for the r‐th time an object of type I appears. Bounds on the distances between the joint distributions ofW1.,Wrwithout and with replacement are

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1978.tb01387.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractLetX1.,Xn1andY1.,Yn1, be two independent random samples from exponential populations. The statistical problem is to test whether or not two exponential populations are the same, based on the order statisticsX[1],.X[r1]andY[1],.Y[rs]where 1 r1n1and 1 r2n2. A new test is given and an asymptotic optimum property of the test is proved.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1978.tb01388.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1978.tb01389.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY